zengfung’s notes
Zeng Fung Liew
2/7/2021
Import data
Univariate EDA
Predictor variables
## year
## 1982 1983 1984 1985 1986 1987 1988
## 48 48 48 48 48 48 48
Question: do we want to round down the drink age? Then make this categorical?
## drinkage
## 18 18.5 19 19.1599998474121
## 12 3 49 1
## 19.25 19.5 19.6700000762939 20
## 2 2 6 20
## 20.25 20.3299999237061 20.5 21
## 1 2 6 232
Response variables
Multivariate EDA
mean response plot:
jail and service have shown slight increase by year.
drinkage have mainly shifted from 18-19 in 1982 to 21 in 1988.
## year
## jail 1982 1983 1984 1985 1986 1987 1988
## no 39 35 34 33 33 34 33
## yes 9 13 14 15 15 14 14## year
## service 1982 1983 1984 1985 1986 1987 1988
## no 43 40 39 38 38 38 37
## yes 5 8 9 10 10 10 10## year
## drinkage_cat 1982 1983 1984 1985 1986 1987 1988
## 18 5 4 3 2 1 0 0
## 19 13 13 13 11 8 1 1
## 20 6 6 6 5 3 3 0
## 21 24 25 26 30 36 44 47Model fitting
Note: goal is to observe whether the type of law implemented to tacker drunk driving can actually prevent fatalities
- panel linear model, using state as panel
not entirely sure how to interpret themodel="within"part.
## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = afatal_prop ~ beertax + jail + service + drinkage,
## data = Fatalities, model = "within", index = "state")
##
## Unbalanced Panel: n = 48, T = 6-7, N = 335
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -0.3434894 -0.0256639 -0.0016049 0.0204173 0.2303012
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## beertax 0.0581056 0.0527138 1.1023 0.2712746
## jailyes 0.1431230 0.0398392 3.5925 0.0003861 ***
## serviceyes -0.1659102 0.0454909 -3.6471 0.0003156 ***
## drinkage -0.0179305 0.0048585 -3.6906 0.0002683 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 0.85673
## Residual Sum of Squares: 0.76982
## R-Squared: 0.10145
## Adj. R-Squared: -0.060485
## F-statistic: 7.98754 on 4 and 283 DF, p-value: 4.1001e-06- lmer model with year as random effect
## Linear mixed model fit by REML ['lmerMod']
## Formula: afatal_prop ~ beertax + jail + service + drinkage_cat + (1 |
## year)
##
## REML criterion at convergence: -722.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1522 -0.6233 -0.1613 0.3997 4.1285
##
## Random effects:
## Groups Name Variance Std.Dev.
## year (Intercept) 0.0003185 0.01785
## Residual 0.0058122 0.07624
## Number of obs: 335, groups: year, 7
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.320246 0.022154 14.455
## beertax 0.020979 0.008871 2.365
## jailyes 0.032811 0.011160 2.940
## serviceyes -0.033128 0.012993 -2.550
## drinkage_cat19 -0.011387 0.022220 -0.512
## drinkage_cat20 -0.006957 0.024473 -0.284
## drinkage_cat21 -0.014572 0.020862 -0.699
##
## Correlation of Fixed Effects:
## (Intr) beertx jailys srvcys drn_19 drn_20
## beertax -0.220
## jailyes -0.168 0.125
## serviceyes -0.033 -0.163 -0.539
## drinkg_ct19 -0.809 -0.020 -0.011 0.107
## drinkg_ct20 -0.749 0.007 0.044 0.065 0.729
## drinkg_ct21 -0.897 0.025 0.088 0.013 0.853 0.782## Analysis of Variance Table
## npar Sum Sq Mean Sq F value
## beertax 1 0.022204 0.022204 3.8202
## jail 1 0.023080 0.023080 3.9710
## service 1 0.040522 0.040522 6.9718
## drinkage_cat 3 0.003903 0.001301 0.2238- regular lm model
state and year are highly significant predictors, but they are not what we’re after
##
## Call:
## lm(formula = afatal_prop ~ beertax + jail + service + drinkage_cat +
## state + year)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.35466 -0.02248 0.00015 0.01619 0.20188
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.385879 0.092139 4.188 3.79e-05 ***
## beertax -0.020500 0.052949 -0.387 0.698931
## jailyes 0.139363 0.038217 3.647 0.000318 ***
## serviceyes -0.127551 0.043811 -2.911 0.003893 **
## drinkage_cat19 0.023605 0.019949 1.183 0.237727
## drinkage_cat20 0.019948 0.021905 0.911 0.363280
## drinkage_cat21 0.017331 0.020887 0.830 0.407388
## stateaz -0.116987 0.080215 -1.458 0.145867
## statear 0.040503 0.061450 0.659 0.510367
## stateca -0.096109 0.086312 -1.114 0.266460
## stateco 0.070782 0.095030 0.745 0.457005
## statect -0.015133 0.080915 -0.187 0.851777
## statede -0.052495 0.082245 -0.638 0.523826
## statefl 0.068501 0.059404 1.153 0.249860
## statega -0.009247 0.050921 -0.182 0.856038
## stateid -0.051942 0.071645 -0.725 0.469073
## stateil -0.067462 0.082035 -0.822 0.411585
## statein -0.041957 0.076659 -0.547 0.584604
## stateia 0.025750 0.070389 0.366 0.714778
## stateks 0.070772 0.074916 0.945 0.345646
## stateky -0.051665 0.080807 -0.639 0.523117
## statela 0.028730 0.060946 0.471 0.637726
## stateme -0.164942 0.064773 -2.546 0.011427 *
## statemd -0.109328 0.079688 -1.372 0.171198
## statema -0.042311 0.076896 -0.550 0.582602
## statemi -0.024254 0.066287 -0.366 0.714729
## statemn -0.069333 0.073858 -0.939 0.348690
## statems 0.173500 0.041241 4.207 3.51e-05 ***
## statemo -0.019088 0.074999 -0.255 0.799294
## statemt -0.129653 0.082326 -1.575 0.116436
## statene -0.077424 0.069420 -1.115 0.265697
## statenv -0.098237 0.084936 -1.157 0.248436
## statenh -0.012067 0.058106 -0.208 0.835642
## statenj -0.142654 0.086280 -1.653 0.099395 .
## statenm -0.084602 0.071488 -1.183 0.237657
## stateny -0.148081 0.083534 -1.773 0.077386 .
## statenc -0.050935 0.032910 -1.548 0.122843
## statend 0.102137 0.071344 1.432 0.153391
## stateoh 0.016797 0.074223 0.226 0.821134
## stateok -0.074009 0.047192 -1.568 0.117973
## stateor -0.096236 0.083853 -1.148 0.252102
## statepa -0.045403 0.077669 -0.585 0.559314
## stateri -0.042844 0.082017 -0.522 0.601822
## statesc 0.024190 0.034280 0.706 0.481013
## statesd -0.058141 0.058771 -0.989 0.323399
## statetn -0.167806 0.083530 -2.009 0.045521 *
## statetx 0.049061 0.068292 0.718 0.473116
## stateut -0.141885 0.060179 -2.358 0.019087 *
## statevt -0.033412 0.060034 -0.557 0.578293
## stateva -0.080420 0.057214 -1.406 0.160972
## statewa -0.174842 0.087810 -1.991 0.047456 *
## statewv -0.169783 0.078554 -2.161 0.031531 *
## statewi -0.019855 0.082927 -0.239 0.810954
## statewy -0.168777 0.095070 -1.775 0.076954 .
## year1983 -0.024575 0.010218 -2.405 0.016829 *
## year1984 -0.030428 0.010314 -2.950 0.003450 **
## year1985 -0.047003 0.010545 -4.457 1.21e-05 ***
## year1986 -0.050025 0.010875 -4.600 6.45e-06 ***
## year1987 -0.062518 0.011635 -5.373 1.65e-07 ***
## year1988 -0.065529 0.012157 -5.390 1.52e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.04943 on 275 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.6802, Adjusted R-squared: 0.6116
## F-statistic: 9.915 on 59 and 275 DF, p-value: < 2.2e-16## Analysis of Variance Table
##
## Response: afatal_prop
## Df Sum Sq Mean Sq F value Pr(>F)
## beertax 1 0.02485 0.024846 10.1703 0.001592 **
## jail 1 0.01760 0.017596 7.2026 0.007721 **
## service 1 0.04768 0.047679 19.5169 1.436e-05 ***
## drinkage_cat 3 0.02312 0.007708 3.1550 0.025295 *
## state 47 1.21970 0.025951 10.6229 < 2.2e-16 ***
## year 6 0.09620 0.016033 6.5628 1.710e-06 ***
## Residuals 275 0.67181 0.002443
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1